Value existence for zero-sum ergodic stochastic differential games
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866908773495341056 |
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| author | Li, Juan Li, Wenqiang Li, Yanwei Zhao, Huaizhong |
| author_facet | Li, Juan Li, Wenqiang Li, Yanwei Zhao, Huaizhong |
| contents | In this paper we investigate two-player zero-sum stochastic differential games with an ergodic payoff, in which the diffusion coefficient does not need to be non-degenerate. We first establish the existence of a viscosity solution to the associated ergodic Hamilton-Jacobi-Bellman-Isaacs equation under a dissipativity condition. With the help of this viscosity solution, we then derive estimates for the upper and the lower ergodic value functions by constructing a series of non-degenerate approximating processes combined with the sup- and inf-convolution techniques. Finally, we prove the existence of a value for the game under the Isaacs condition and provide its representation formulae. As an application, we study the pollution accumulation problem with a long-run average social welfare to illustrate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_15894 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Value existence for zero-sum ergodic stochastic differential games Li, Juan Li, Wenqiang Li, Yanwei Zhao, Huaizhong Optimization and Control Probability 49L25, 91A15, 93E20 In this paper we investigate two-player zero-sum stochastic differential games with an ergodic payoff, in which the diffusion coefficient does not need to be non-degenerate. We first establish the existence of a viscosity solution to the associated ergodic Hamilton-Jacobi-Bellman-Isaacs equation under a dissipativity condition. With the help of this viscosity solution, we then derive estimates for the upper and the lower ergodic value functions by constructing a series of non-degenerate approximating processes combined with the sup- and inf-convolution techniques. Finally, we prove the existence of a value for the game under the Isaacs condition and provide its representation formulae. As an application, we study the pollution accumulation problem with a long-run average social welfare to illustrate our theoretical results. |
| title | Value existence for zero-sum ergodic stochastic differential games |
| topic | Optimization and Control Probability 49L25, 91A15, 93E20 |
| url | https://arxiv.org/abs/2106.15894 |